School matching in Amsterdam: Top Trading Cycles reconsidered

Abstract

For years, the matching of students to schools in Amsterdam has been a tough challenge. Especially in 2015, when the matching algorithm DA-MTB was used, many families were displeased with the results. By running simulations using real data from the Amsterdam matching process, the different matching mechanisms can be compared. Boston, DA-MTB, DA-STB and TTC are analysed on their theoretical properties and performance on efficiency and fairness. The Boston mechanism performs best in placing students at their first choice, but does place many students at a school they do not prefer. DA-MTB maximizes the number of students assigned to a school in their top-5, but assigns the smallest number of students to their first choice. When comparing DA-STB and TTC, they create a similar assignment, but TTC places more students at schools for every rank in the preference list and creates a Pareto efficient assignment. TTC can be adapted to the admission problem in which school-specific priorities exist by applying its assigning process only to a subset of the students. TTC does create instances of justified envy, but given its properties and results seems a better fit to the Amsterdam school problem than DA-STB.